AS/A2 Pure 2 Pure 3

P1 Topic 2: Algebra
The factor theorem 2
The factor theorem states that:
If f(x) is a polynomial and f(a) = 0, then x-a is a factor of f(x).

Show that (x+3) is a factor of f(x) = 2x3+5x2-8x-15

Show that (x-2) is a factor of f(x) = x3-5x2+4x+4

Summary The factor theorem is a very useful result. It helps to get answers in an easy and quick way, and it often means (as the above examples show) that you can avoid using "algebraic long division". This page uses WebEQ. To speed up downloading you can install this WebEQ Math Viewer . Click on the Math Viewer icon and you will be taken to the download site.